A 3 x 3 magic square is a 3 x 3 grid filled with distinct numbers from 1 to 9 such that each row, column, and both diagonals all have the same sum. Write a function (along with helper functions) which checks if a 3 x 3 matrix is a magic square. You are required to write just the function(s). Assume that user input is already provided.

Example Input matrix = [ [4, 3, 8], [9, 5, 1], [2, 7, 6] ] Output: True please write the program in c++